Question: Solve for $x$ and $y$ using elimination. ${4x+6y = 64}$ ${5x-5y = 5}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $5$ and the bottom equation by $6$ ${20x+30y = 320}$ $30x-30y = 30$ Add the top and bottom equations together. $50x = 350$ $\dfrac{50x}{{50}} = \dfrac{350}{{50}}$ ${x = 7}$ Now that you know ${x = 7}$ , plug it back into $\thinspace {4x+6y = 64}\thinspace$ to find $y$ ${4}{(7)}{ + 6y = 64}$ $28+6y = 64$ $28{-28} + 6y = 64{-28}$ $6y = 36$ $\dfrac{6y}{{6}} = \dfrac{36}{{6}}$ ${y = 6}$ You can also plug ${x = 7}$ into $\thinspace {5x-5y = 5}\thinspace$ and get the same answer for $y$ : ${5}{(7)}{ - 5y = 5}$ ${y = 6}$